UNDERSTANDING POWER FACTOR

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Marcus Richards
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1 ALICATION NOTE UNDERTANDING OWER FACTOR by L. Wuidart 1. INTRODUCTION The majority of electronics designers do not worry about ower Factor (F); F is something that you learnt one day at school in your electrotechnics course as being the cos οf ϕ, the phase angle between the voltage and current waveforms. However, this conventional definition is only valid when considering ideal sinusoidal signals for both current and voltage waveforms, and in reality most off-line power supplies draw a nonsinusoidal current. Many off-line systems will typically have a front end section consisting of a rectifier bridge and an input filter capacitor, which act as a peak detector - see figure 1. A current flows to charge the capacitor only when the instantaneous AC voltage exceeds the voltage of the capacitor. A single phase off-line supply draws a current pulse during a small fraction of the half-cycle duration. Between those current peaks, the load draws the energy stored in the input capacitor. The phase lag ϕ and also the harmonic content of the pulsed current waveform produce additional RM currents, affecting the real power available from the mains. o ower Factor is much more than cos ϕ! The.F. value measures how much the mains efficiency is affected by both the phase lag ϕ and the harmonic content of the input current. In this context, the European tandard EN only defines the limit of current harmonics in mains supplied equipment. AN523/1093 1/5

2 Figure 1: Full-Wave Rectifier I mains LOAD V DC V DC V mains V mains I mains T/2 T t 2. THEORETICAL MEANING The ower Factor is defined by:.f. = = REAL OWER AARENT OWER 2.1 Ideal sinusoidal signals For ideal sinusoidal voltage and current waveforms, if there is a phase difference ϕ between the voltage and current waveforms, the total apparent power can be modelled as being composed of two components: one in phase with the input voltage, and the other 90 out of phase (in quadrature) with it - see figure 2. Then by definition,.f. = = CO ϕ Figure 2: ower vectors of ideal sinusoidal signals ϕ = V RM. I RM CO ϕ: In-hase or Real ower Q = V RM. I RM IN ϕ: Reactive or Quadrative ower = V RM. I RM : Total Apparent ower Q 2.2 Non-ideal sinusoidal current Assuming that the mains voltage is an ideal sinusoidal voltage waveform, its RM value is: V RM V peak = 2 If the current has been distorted in some way (for example as in figure 1) into a periodic non-sinusoidal waveform, applying a Fourier transform gives: I RM(total) = I 0 + I 2 1RM + I 2 2RM I 2 nrm where I 0 is the DC component of the current, I 1RM the fundamental of the RM current (that is the component at the frequency of the voltage input) and I 2RM... I nrm are the harmonics created by the distortion. For a pure AC signal, there is no DC component and so I 0 = 0. The fundamental of the RM current can be modelled as in section 2.1 above as an inphase component I 1RM and a quadrature component I 1RMQ, and so the RM current can be expressed as: I RM(total) = I 0 + I 2 1RM + I 2 1RM Q + Σ I 2 nrm Then, the Real ower is given by the RM voltage multiplied by the in-phase current: = V RM. I 1RM n=2 2/5

3 As ϕ 1 is the displacement angle between the input voltage and the in-phase component of the fundamental current: so I 1RM = I 1RM CO ϕ 1 = V RM. I RM CO ϕ 1 As the total apparent power is given by: = V RM. I RM total the ower Factor can be calculated as :.F. = CO = I 1 RM. 1 I RM (total) If the phase angle between I 1RM and I RM(total) is defined as θ: CO θ = I 1 RM I RM (total) θ is linked to the harmonic content of the current; as the harmonic content of I RM(total) approaches zero, θ approaches 0 and cos θ approaches ummary Finally then, the ower Factor can be expressed as:.f. = CO θ. CO ϕ 1 and the representation of the power vectors becomes that shown in figure 3. ϕ 1 is the conventional displacement angle (phase lag) between the voltage and the fundamental component of the current, while θ is the distortion angle caused by the harmonic content of the current. Both the reactive power, Q, and the distortion power, D, produce extra RM currents, giving additional losses and reducing the efficiency of the mains supply network. Figure 3: ower vectors with non-sinusoidal signals. ϕ1 θ 1 D Q = Real ower = V RM. I RM. CO ϕ Q = Reactive ower = V RM. I RM. IN ϕ 1 = Apparent Fundamental ower = V RM. I 1RM D = Distortion ower = V RM. Σ I 2 nrm n=2 = TOTAL AARENT OWER =V RM. I RM (total) 3/5

4 Improving the ower Factor means reducing both elements: ϕ 1 0 means CO ϕ 1 1: reduction of the phase lag between I and V, θ 0 means CO θ 1: reduction of harmonic content of I. 3. RACTICAL IMLICATION OF OWER FACTOR 3.1 Benefits of reduced ower Factor Both the user and the electricity supply company can benefit from a reduction in ower Factor. Adding a FC also reduces the component costs in a downstream converter Benefits to the user At the minimum line voltage (85V AC ), a standard 115V AC wall socket should be able to deliver the nominal 15A to a common load. However, an M without a ower Factor Corrector (FC), which will typically have a ower Factor of 0.6, reduces the available current to around 9A. As an example, a single wall socket will supply four 280W computers equipped with FCs, but only two without Benefits to the distribution company Both the reactive power Q and the distortion power D give rise to extra RM currents, significantly reducing the efficiency of the mains supply network. This means that the copper distribution wires must be thicker than would otherwise be necessary. Delivering power at frequencies other than the line frequency (ie the distortion power D) also causes difficulties. The distortion disturbs the zero voltage crossing detection systems, and generates overcurrent in the neutral line and resonant overvoltages. In Europe, the standard EN and the international project IEC limit the harmonic content of the current of mains supplied equipment Reduction of component costs in the downstream converter For the same output power capability, a conventional converter using an input mains voltage doubler has primary RM current 1.8 times higher than one employing a FC regulator. Consequently, if a FC is used in a system using ower MOFET switches, the on-resistance (R D(ON) ) of the switches can be up to three times higher than in a system without FC, allowing significantly cheaper parts to be used. The size of the converter transformer can be reduced not only because the thickness of the windings is smaller, but also because of the regulation of the DC bulk voltage delivered by the FC pre-regulator. The FC provides an automatic mains selection on a wide range of voltages from 85V AC up to 265V AC. Compared to the conventional doubler front-end section the same hold-up time can be achieved with a bulk storage capacitor 6 times smaller. For example, to achieve a 10ms hold-up time, a 100W converter in doubler operation requires a series combination of two 440µF capacitors without a FC, but only a single 130µF with. 3.2 RFI filter However, the size and cost optimisation of the FC has to take the RFI filter into consideration. A FC circuit generates more high frequency interference to the mains than a conventional rectifier front-end - see figure 4. Thus the use of a FC means that additional filtering is required. For this reason, modulation techniques and mode of operation for the FC have to be carefully adapted to the requirements of the application. 4/5

5 Figure 4: M with (a) conventional rectifier front-end, and (b) FC front-end. maller EMI filter C i 220µF Larger EMI filter C i 0.1µF FC 4. CONCLUION For new designs, M designers will have to take into account the IEC standard. In practice, this will require the use of a FC on the front end of much mains supplied equipment. The additional cost of the FC is compensated by the significant reduction in the cost of components for the downstream converter. The FC also provides additional functions such as automatic mains voltage selection and constant output voltage. Information furnished is believed to be accurate and reliable. However, TMicroelectronics assumes no responsibility for the consequences of use of such information nor for any infringement of patents or other rights of third parties which may result from its use. No license is granted by implication or otherwise under any patent or patent rights of TMicroelectronics. pecification mentioned in this publication are subject to change without notice. This publication supersedes and replaces all information previously supplied. TMicroelectronics products are not authorized for use as critical components in life support devices or systems without express written approval of TMicroelectronics. The T logo is a trademark of TMicroelectronics 1999 TMicroelectronics - rinted in Italy - All Rights Reserved TMicroelectronics GROU OF COMANIE Australia - Brazil - China - Finland - France - Germany - Hong Kong - India - Italy - Japan - Malaysia - Malta - Morocco - ingapore - pain - weden - witzerland - United Kingdom - U..A. 5/5

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